SOLUTION: The smaller of two number is two-thirds of the larger, & the sum of their reciprocals is 1/6. What are the numbers?

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Question 97184: The smaller of two number is two-thirds of the larger, & the sum of their reciprocals is 1/6. What are the numbers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The smaller of two numbers is two-thirds of the larger,
One number = x; smaller number = %282x%29%2F3
:
the sum of their reciprocals is 1/6.
1%2Fx + 3%2F%282x%29 = 1%2F6
:
What are the numbers?
:
The common denominator would be 6x, multiply equation by 6x
6x*1%2Fx + 6x*3%2F%282x%29 = 6x*1%2F6
:
Cancel the denominators leaving:
6(1) + 3(3) = x(1)
6 + 9 = x
x = 15 is one number
:
The smaller:
2%2F3*15 = 10
:
:
Check solution in original equation:
1%2F15 + 1%2F10%29 = 1%2F6
2%2F30 + 3%2F30%29 = 5%2F30